Different camera sizes in same file
I can't rule it out 100% but I would be very surprised if you could do this per camera. You can change the sensor width and height in the camera settings, but that should not change the aspect in the rendering. 

The only solution that comes to mind is a script that hardcodes the desired resolution (and with that the aspect ratio) for each camera and set it up as a driver. Meaning when you hit render it will check which camera is active and assign the resolution that you referenced to that camera.
Let me know if that is an option, then I would try to work out that script. Also: untested, there might be one more step to that. Worst comes to worst we create a tiny script that acts as a render button but does the adaption to your scene before render (that one will work for sure).